package edu.princeton.cs.algs4;

import edu.princeton.cs.stdlib.StdIn;
import edu.princeton.cs.stdlib.StdOut;

/*************************************************************************
 * Compilation: javac BST.java Execution: java BST
 * 
 * A symbol table implemented with a binary search tree.
 * 
 * % more tiny.txt S E A R C H E X A M P L E
 * 
 * % java BST < tiny.txt A 8 C 4 E 12 H 5 L 11 M 9 P 10 R 3 S 0 X 7
 * 
 *************************************************************************/

public class BST<Key extends Comparable<Key>, Value> {
	private Node root; // root of BST

	private class Node {
		private Key key; // sorted by key
		private Value val; // associated data
		private Node left, right; // left and right subtrees
		private int N; // number of nodes in subtree

		public Node(Key key, Value val, int N) {
			this.key = key;
			this.val = val;
			this.N = N;
		}
	}

	// is the symbol table empty?
	public boolean isEmpty() {
		return size() == 0;
	}

	// return number of key-value pairs in BST
	public int size() {
		return size(root);
	}

	// return number of key-value pairs in BST rooted at x
	private int size(Node x) {
		if (x == null)
			return 0;
		else
			return x.N;
	}

	/***********************************************************************
	 * Search BST for given key, and return associated value if found, return
	 * null if not found
	 ***********************************************************************/
	// does there exist a key-value pair with given key?
	public boolean contains(Key key) {
		return get(key) != null;
	}

	// return value associated with the given key, or null if no such key exists
	public Value get(Key key) {
		return get(root, key);
	}

	private Value get(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			return get(x.left, key);
		else if (cmp > 0)
			return get(x.right, key);
		else
			return x.val;
	}

	/***********************************************************************
	 * Insert key-value pair into BST If key already exists, update with new
	 * value
	 ***********************************************************************/
	public void put(Key key, Value val) {
		if (val == null) {
			delete(key);
			return;
		}
		root = put(root, key, val);
		assert isBST();
	}

	private Node put(Node x, Key key, Value val) {
		if (x == null)
			return new Node(key, val, 1);
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			x.left = put(x.left, key, val);
		else if (cmp > 0)
			x.right = put(x.right, key, val);
		else
			x.val = val;
		x.N = 1 + size(x.left) + size(x.right);
		return x;
	}

	/***********************************************************************
	 * Delete
	 ***********************************************************************/

	public void deleteMin() {
		if (isEmpty())
			throw new RuntimeException("Symbol table underflow");
		root = deleteMin(root);
		assert isBST();
	}

	private Node deleteMin(Node x) {
		if (x.left == null)
			return x.right;
		x.left = deleteMin(x.left);
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	public void deleteMax() {
		if (isEmpty())
			throw new RuntimeException("Symbol table underflow");
		root = deleteMax(root);
		assert isBST();
	}

	private Node deleteMax(Node x) {
		if (x.right == null)
			return x.left;
		x.right = deleteMax(x.right);
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	public void delete(Key key) {
		root = delete(root, key);
		assert isBST();
	}

	private Node delete(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			x.left = delete(x.left, key);
		else if (cmp > 0)
			x.right = delete(x.right, key);
		else {
			if (x.right == null)
				return x.left;
			if (x.left == null)
				return x.right;
			Node t = x;
			x = min(t.right);
			x.right = deleteMin(t.right);
			x.left = t.left;
		}
		x.N = size(x.left) + size(x.right) + 1;
		return x;
	}

	/***********************************************************************
	 * Min, max, floor, and ceiling
	 ***********************************************************************/
	public Key min() {
		if (isEmpty())
			return null;
		return min(root).key;
	}

	private Node min(Node x) {
		if (x.left == null)
			return x;
		else
			return min(x.left);
	}

	public Key max() {
		if (isEmpty())
			return null;
		return max(root).key;
	}

	private Node max(Node x) {
		if (x.right == null)
			return x;
		else
			return max(x.right);
	}

	public Key floor(Key key) {
		Node x = floor(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	private Node floor(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp == 0)
			return x;
		if (cmp < 0)
			return floor(x.left, key);
		Node t = floor(x.right, key);
		if (t != null)
			return t;
		else
			return x;
	}

	public Key ceiling(Key key) {
		Node x = ceiling(root, key);
		if (x == null)
			return null;
		else
			return x.key;
	}

	private Node ceiling(Node x, Key key) {
		if (x == null)
			return null;
		int cmp = key.compareTo(x.key);
		if (cmp == 0)
			return x;
		if (cmp < 0) {
			Node t = ceiling(x.left, key);
			if (t != null)
				return t;
			else
				return x;
		}
		return ceiling(x.right, key);
	}

	/***********************************************************************
	 * Rank and selection
	 ***********************************************************************/
	public Key select(int k) {
		if (k < 0 || k >= size())
			return null;
		Node x = select(root, k);
		return x.key;
	}

	// Return key of rank k.
	private Node select(Node x, int k) {
		if (x == null)
			return null;
		int t = size(x.left);
		if (t > k)
			return select(x.left, k);
		else if (t < k)
			return select(x.right, k - t - 1);
		else
			return x;
	}

	public int rank(Key key) {
		return rank(key, root);
	}

	// Number of keys in the subtree less than x.key.
	private int rank(Key key, Node x) {
		if (x == null)
			return 0;
		int cmp = key.compareTo(x.key);
		if (cmp < 0)
			return rank(key, x.left);
		else if (cmp > 0)
			return 1 + size(x.left) + rank(key, x.right);
		else
			return size(x.left);
	}

	/***********************************************************************
	 * Range count and range search.
	 ***********************************************************************/
	public Iterable<Key> keys() {
		return keys(min(), max());
	}

	public Iterable<Key> keys(Key lo, Key hi) {
		Queue<Key> queue = new Queue<Key>();
		keys(root, queue, lo, hi);
		return queue;
	}

	private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
		if (x == null)
			return;
		int cmplo = lo.compareTo(x.key);
		int cmphi = hi.compareTo(x.key);
		if (cmplo < 0)
			keys(x.left, queue, lo, hi);
		if (cmplo <= 0 && cmphi >= 0)
			queue.enqueue(x.key);
		if (cmphi > 0)
			keys(x.right, queue, lo, hi);
	}

	public int size(Key lo, Key hi) {
		if (lo.compareTo(hi) > 0)
			return 0;
		if (contains(hi))
			return rank(hi) - rank(lo) + 1;
		else
			return rank(hi) - rank(lo);
	}

	/*************************************************************************
	 * Check integrity of BST
	 *************************************************************************/
	// is this tree a BST?
	private boolean isBST() {
		if (isEmpty())
			return true;
		if (!isBinaryTree())
			StdOut.println("Subtree counts not consistent");
		if (!isOrdered())
			StdOut.println("Not in symmetric order");
		if (!hasNoDuplicates())
			StdOut.println("Has duplicate keys");
		if (!isRankConsistent())
			StdOut.println("Rank not consistent");
		return isBinaryTree() && isOrdered() && hasNoDuplicates()
				&& isRankConsistent();
	}

	// are the size fields correct (and consequently is it a binary tree)
	private boolean isBinaryTree() {
		return isBinaryTree(root);
	}

	private boolean isBinaryTree(Node x) {
		if (x == null)
			return true;
		if (x.N != size(x.left) + size(x.right) + 1)
			return false;
		return isBinaryTree(x.left) && isBinaryTree(x.right);
	}

	// does this binary tree satisfy symmetric order?
	private boolean isOrdered() {
		assert isBinaryTree();
		return isOrdered(root, min(), max());
	}

	// are all the values in the BST rooted at x between min and max, and
	// recursively?
	private boolean isOrdered(Node x, Key min, Key max) {
		if (x == null)
			return true;
		if (less(x.key, min) || less(max, x.key))
			return false;
		return isOrdered(x.left, min, x.key) && isOrdered(x.right, x.key, max);
	}

	// check that there are no duplicate keys
	// precondition: inorder traversal gives keys in order
	private boolean hasNoDuplicates() {
		assert isOrdered();
		for (int i = 1; i < size(); i++) {
			if (select(i).compareTo(select(i - 1)) == 0)
				return false;
		}
		return true;
	}

	// check that ranks are consistent
	private boolean isRankConsistent() {
		for (int i = 0; i < size(); i++)
			if (i != rank(select(i)))
				return false;
		for (Key key : keys())
			if (key.compareTo(select(rank(key))) != 0)
				return false;
		return true;
	}

	private boolean less(Key x, Key y) {
		return x.compareTo(y) < 0;
	}

	/*****************************************************************************
	 * Test client
	 *****************************************************************************/
	public static void main(String[] args) {
		BST<String, Integer> st = new BST<String, Integer>();
		for (int i = 0; !StdIn.isEmpty(); i++) {
			String key = StdIn.readString();
			st.put(key, i);
		}
		for (String s : st.keys())
			StdOut.println(s + " " + st.get(s));
	}
}
